Model Selection and Inference in Variational Longitudinal Distributed Lag Models

Flight-related health effects are a growing area of environmental health research with most work examining the concurrent impact of in-flight exposure on cardiac health. One understudied area is on the post-flight effects of in-flight exposures. Studies on the health effects of flight often collect a range of repeatedly sampled, time-varying exposure measurements both under crossover and longitudinal sampling designs. A natural choice to model the relationship of these lagged exposures on post-flight outcomes is the distributed lag model (DLM). However, longitudinal DLMs are a lightly studied class of models. In this article, we propose a class of models for analyzing longitudinal DLMs where the random effects can incorporate more general structures including random lags that arise from repeatedly sampling lagged exposures. We develop variational Bayesian algorithms to estimate model components under differing random effect structures, derive a variational AIC for model selection between these structures, and show how the converged variational estimates can fit into a framework for testing for the difference between two semiparametric curves. We then investigate the post-flight effects of in-flight, lagged exposures on heart health. We also perform simulation studies to evaluate the operating characteristics of our models.